A ring R is called a right weakly V-ring (briefly, a right WV-ring) if every simple right R-
module is X-injective, where X is any cyclic right R-module with XR≇ RR. In this note, we …

We introduce the class of “right almost V-rings” which is properly between the classes of
right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R …

We say that a ring R is a right RDV-ring if each simple right R-module is RD-injective. In this
paper, we study the notion of RDV-rings which is a non-trivial generalization of V-rings and …

Kaplansky [11] noticed that a commutative ring is (von Neumann) regular if and only if it is a
V-ring, that is, each simple module over the ring is injective. However in the general case …

Right V-rings R with infinitely generated right socle SOC (RR) such that R/SOC (RR) is a
division ring are characterized as those non-noetherian rings over which a cyclic right …

Right ue-rings (rings with the property of the title, ie, with the maximality of the right socle)
are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a …

In this paper, we extend some results of V rings to GP-V rings and GP-V'rings. Some
characterizations of strongly regular rings are obtained. We show that (1) R is strongly …

ABSTRACT. Let R be a ring with identity and M a right R-module. Let E (M) denote the
injective hull of M and Z'(M):= MORadE (M). We say M has*-radical if Z (M)= RadM. In this …

It will be shown that a particular quotient ring of a ring $ R $ is a nontrivial $ V $-ring if $ R $
is a special kind of a right hereditary, right Noetherian ring. Another result states that all …

In this note, we find similar characteristic properties in terms of certain intersections of
maximal left ideals for the following classes of rings:(1) Left V-rings;(2) Left fV-rings;(3) Left …